On the Critical Behavior of the Uniform Susceptibility of a Fermi Liquid Near an Antiferromagnetic Transition with Dynamic Exponent $ z = 2$

Details On the Critical Behavior of the Uniform Susceptibility of a Fermi Liquid Near an Antiferromagnetic Transition with Dynamic Exponent $ z = 2$ On the Critical Behavior of the Uniform Susceptibility of a Fermi Liquid Near an Antiferromagnetic Transition with Dynamic Exponent $ z = 2$

1994-11-04

arxiv.org/abs/cond-mat/9411021v1

Physics

Condensed Matter

12 pages, uuencoded Postscript file

Scientific paper

10.1103/PhysRevB.51.16151

We compute the leading behavior of the uniform magnetic susceptibility, $\chi$, of a Fermi liquid near an antiferromagnetic transition with dynamic exponent $z=2$. Our calculation clarifies the role of triangular ``anomaly'' graphs in the theory and justifies the effective action used in previous work \cite{Hertz}. We find that at the $z=2$ critical point of a two dimensional material, $lim_{q \rightarrow 0} \chi (q,0) = \chi_0 - D T$ with $\chi_0$ and $D$ nonuniversal constants. For reasonable band structures we find that in a weak coupling approximation $D$ is small and positive. Our result suggests that the behavior observed in the quantum critical regime of underdoped high-$T_c$ superconductors are difficult to explain in a $z=2$ theory.

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